A digital communication system typically involves transmitting a modulated data stream from a transmitter to a receiver over a communication channel. The communication channel can include a microwave radio link, a satellite channel, a fiber optic cable, or a copper cable to provide some examples. A communication channel contains a propagation medium that the modulated data stream passes through before reception by the receiver.
The propagation medium of the communication channel introduces distortion into the transmitted modulated data stream causing a received modulated data stream to differ from the transmitted modulated data stream. Noise, signal strength variations known as fading, phase shift variations, or multiple path delays known as multi-path propagation can introduce distortion into the transmitted modulated data stream. For example, transmission over a multiplicity of paths of different and variable lengths, or rapidly varying delays in the propagation medium from the transmitter to the receiver, may cause a change in the amplitude and/or phase of the transmitted modulated data stream.
Digital communication systems use an adjustable filter in the forum of an equalizer to reduce the effect of the distortion caused by the communication channel. A receiver may directly set equalization filter coefficients for known or measured communication channels. However, in most situations the characteristics of the communication channel are not known in advance and therefore require the use of an adaptive equalizer. Adaptive equalizers derive adjustable filter coefficients from a received demodulated data stream.
A symmetric or a complex adaptive equalizer is an equalizer whereby the received demodulated data stream may be represented as complex samples. Each complex sample includes a real component and an imaginary component. The output of the complex adaptive equalizer is also complex with a real component and an imaginary component. The imaginary component and the real component of the equalized output are determined by combining a multiplication between a delayed version of the received demodulated data stream and adjustable filter coefficients of the equalizer. This complex multiplication requires two complex multiplications and one real addition for each component of the equalized output for a total of four real multiplications and two real additions.
One way of understanding the complex multiplication in conventional equalization techniques is to express it as a constrained two by two real matrix multiplication. The corresponding matrix used to perform the multiplication is a two by two matrix containing four real numbers. In a symmetric complex equalizer, this matrix may be constrained such that the diagonal elements are equal and the off diagonal elements are the negatives of each other to provide an example.
However, an asymmetric equalizer may relax the constraints of the two by two matrix by replacing the complex multiplication may with a general two by two real matrix multiplication. The asymmetric equalizer implements the two by two matrix using any four real numbers. The symmetric equalizer may reduce the effect of the distortion caused by the communication channel so long as the characteristics of the communication system are linear. However, in practice, some effects of the communication channel as well as distortion caused by the transmitter and/or receiver are not linear. For example, in a multi-channel communication signal, residual signals resulting from a frequency-inverted duplicate or mirror image of a corresponding signal of interest or one or more neighboring information channels within the multi-channel information signal are some examples of nonlinear effects requiring the use of an asymmetric equalizer.
Therefore what is needed is an adaptive equalizer that is capable of compensating for the non-linear effects resulting from the transmitter, the receiver, and/or the communication channel in a communication system.
The present invention will now be described with reference to the accompanying drawings. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements. The drawing in which an element first appears is indicated by the leftmost digit(s) in the reference number.